The family of curves defined by y = kx^3 represents:

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Question: The family of curves defined by y = kx^3 represents:

Options:

Correct Answer: Cubic curves

Solution:

The equation y = kx^3 represents a family of cubic curves.

The family of curves defined by y = kx^3 represents:

The family of curves defined by y = kx^3 represents:

Step 1: Identify the equation given, which is y = kx^3.
Step 2: Recognize that 'k' is a constant that can take different values.
Step 3: Understand that changing the value of 'k' will change the shape of the curve.
Step 4: Realize that for each different value of 'k', you get a different curve, but they all have the same general form (cubic).
Step 5: Conclude that all these curves together form a 'family of curves' because they are related by the same equation with varying 'k'.

Cubic Functions – The equation y = kx^3 represents a family of cubic functions, where 'k' is a constant that affects the shape and position of the curve.